Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun Equality of measure.
  • noun Equality of elevation above sea level.
  • noun Mathematics A function between metric spaces which preserves distances, such as a rotation or translation in a plane.
  • noun Biology A proportional change in the size of a part or parts of an organism as the organism grows.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun mathematics A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their pre-images.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • noun equality of elevation above sea level
  • noun equality of measure (e.g., equality of height above sea level or equality of loudness etc.)
  • noun the growth rates in different parts of a growing organism are the same
  • noun a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points

Etymologies

from Wiktionary, Creative Commons Attribution/Share-Alike License

From iso- and -metry.

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Examples

  • The metric has time dependent metric elements, which means there is no Killing isometry which defines energy conservation as a symmetry of the spacetime.

    The Known Universe (Video) | Universe Today 2009

  • Temperature-mediated transitions between isometry and allometry in a colonial, modular invertebarte.

    Biology of early life stage of tropical reef corals 2008

  • Further momentum is an isometry of this spacetime, so momentum is conserved.

    Does Space Expand? Sean 2008

  • The metric coefficients are time dependent, and this precludes the existence of a Killing vector K_t that defines an isometry and energy conservation law.

    Being a Heretic is Hard Work Sean 2008

  • In effect cosmologies in their lack of such isometry permits the creation of momentum and energy — aka the big bang.

    Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask Sean 2008

  • With a few [extremely non-generic] exceptions, namely the ones with maximal isometry groups, one can say definitely whether they are expanding or not.

    Does Space Expand? Sean 2008

  • This process of being dragged along is due to a symmetry (isometry) of space which preserves momentum.

    Be vewwwwy vewwwwy quiet…. Julianne 2008

  • (M², g²ab), respectively, and if there exists an isometry

    Time Machines Earman, John 2004

  • Does it follow, as we would want determinism to guarantee, that Ψ is extendible to an isometry from

    Time Machines Earman, John 2004

  • (M*, g*ab) violates the condition that determinism was supposed to guarantee as Ψ is not extendible to an isometry from D+ (Σ) onto

    Time Machines Earman, John 2004

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